Comparison of Methods for Identifying Differential Step Functioning with Polytomous Item Response Data

Much research has been devoted to identification of differential item functioning (DIF), which occurs when the item responses for individuals from two groups differ after they are conditioned on the latent trait being measured by the scale. There has been less work examining differential step functioning (DSF), which is present for polytomous items when the conditional likelihood of responses to specific categories differ between groups. DSF impacts estimation of the measured trait and reduces the effectiveness of standard DIF detection methods. The purpose of this simulation study was to extend upon earlier work by comparing several methods for detecting the presence of DSF in polytomous items, including an approach based on the lasso estimation of the generalized partial credit model. Results show that the lasso GPCM technique controlled the Type I error rate while yielding power rates somewhat lower than logistic regression and the MIMIC model, which were not able to control the Type I error rate in some conditions. An empirical example is also presented, and implications of this study for practice are discussed.